Topological Superconductivity in Rashba Superlattices

Abstract

Recent studies have shown that low dimensional semiconducting nanomaterials with a non trivial geometry possess interesting topological properties. In fact, as a consequence of the curved geometry, non trivial insulating phases can arise in those systems. In this thesis we analyse the influence of the curvature properties on the topological superconducting phase. We start by considering a model designed to reproduce topological superconductivity in a straight 1D semiconducting nanowire. Superconductivity is induced by proximity with a conventional superconductor and the presence of Rashba spin orbit coupling and an external magnetic field in orthogonal directions allows for the realization of a topological superconducting phase in the semiconductor. Consequently, we analyse the dynamical properties of an electron moving in a curved nanowire, showing that they result in a local spin orbit coupling, inducing a local canting of the electron spin. Finally, we study the robustness of the topological phase of the system against the perturbation introduced by the curvature, and we find that the topological phase is suppressed as a result of the presence of the local spin orbit coupling.